A190145 Decimal expansion of Sum_{k>=1} (1/Product_{j=1..k} j^j'), where n' is the arithmetic derivative of n.

1, 6, 6, 7, 4, 4, 7, 9, 3, 5, 8, 0, 3, 6, 9, 3, 9, 0, 5, 5, 8, 0, 5, 6, 7, 5, 1, 2, 8, 7, 3, 3, 9, 6, 0, 2, 0, 3, 9, 4, 4, 7, 8, 0, 1, 1, 3, 8, 1, 7, 7, 1, 6, 7, 0, 0, 5, 3, 7, 2, 8, 2, 2, 7, 6, 2, 0, 5, 8, 9, 3, 2, 9, 0, 2, 5, 2, 7, 7, 9, 1, 7, 0, 2, 4, 5, 2, 5, 4, 9, 9, 7, 7, 0, 8, 8, 1, 2, 2, 4, 8, 2, 4, 1, 6, 2, 6, 3, 3, 6, 8, 6, 1, 5, 1, 1, 1, 8, 9, 1

Offset

1,2

References

1

Links

Table of n, a(n) for n=1..120.

Example

1/1^1' + 1/(1^1' * 2^2') + 1/(1^1' * 2^2' * 3^3') + 1/(1^1' * 2^2' * 3^3' * 4^4') + ... = 1 + 1/2 + 1/6 + 1/1536 + ... = 1.6674479358036...

Maple

with(numtheory);
P:=proc(i)
local a, b, c, d, f, n, p, pfs, s;
a:=0; b:=1;
for n from 2 by 1 to i do
  pfs:=ifactors(n)[2];
  f:=n*add(op(2, p)/op(1, p), p=pfs);
  b:=b*n^f; a:=a+1/b;
od;
print(evalf(a, 300));
end:
P(1000);

Mathematica

digits = 120; d[0] = d[1] = 0; d[n_] := d[n] = n*Total[Apply[#2/#1 &, FactorInteger[n], {1}]]; p[m_] := p[m] = Sum[1/Product[j^d[j], {j, 2, k}], {k, 1, m}] // RealDigits[#, 10, digits] & // First; p[digits]; p[m = 2*digits]; While[p[m] != p[m/2], m = 2*m]; p[m] (* Jean-François Alcover, Feb 21 2014 *)

Crossrefs

Cf. A003415, A190144, A190146, A190147.

Sequence in context: A196737 A070058 A160057 * A351214 A195103 A345685

Adjacent sequences: A190142 A190143 A190144 * A190146 A190147 A190148

Keyword

nonn,cons

Author

Paolo P. Lava, May 05 2011

Status

approved